Relation between the Solution-State Behavior of Self-Assembled

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Relation between the Solution-State Behavior of Self-Assembled Monolayers on Nanoparticles and Dispersion of Nanoparticles in Organic Solvents Toshihiko Arita,†,* Jungwoo Yoo,† and Tadafumi Adschiri‡ † ‡

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan WPI Research Center: Advanced Institute of Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan

bS Supporting Information ABSTRACT: The solution-state property of three-dimensional self-assembled monolayers (3D SAMs) on CeO2 nanoparticles (NPs) has been found to seriously affect dispersion of the NPs. The chain length and solvent-dependent changes in the properties of SAMs were investigated by using various n-alkanoic acid SAMs on CeO2 NPs and various nonpolar organic solvents. NMR and DSC were employed to analyze solution-state behavior of the 3D SAMs. A scaling approach on the chain length and the grafting density of the SAMs could characterize the behavior of SAMs in solution: whether the SAMs were swelling or not. The solvent quality (good or poor) for SAMs was also important for the swelling of the SAMs. In addition, the volume of the solvent molecule was also a critical parameter. The swollen SAMs could provide effective repulsion to overcome van der Waals attraction between NPs. Combining our scaling analysis on solution-state behavior of the 3D SAMs and the experimental results of dispersion of the CeO2 NPs, a criterion for the 3D SAMs to obtain well-dispersed surface-modified NPs was proposed.

’ INTRODUCTION Nanometer-sized particles (nanoparticles; NPs) have received tremendous attention in nanoscience and technology in terms of their size-dependent optical, magnetic, electric, and mechanical properties. Because of their special properties, NPs have been good materials for manufacturing nanosized devices. However, the aggregation of NPs derived from high surface energy density of NPs spoils the particular size-dependent properties. Therefore, stable dispersion of NPs is the most primary issue being established in NP-related studies. One of the most widely used methods to obtain well-dispersed NPs is surface modification by organic molecules.1-5 However, it is still difficult to obtain a perfectly and stable NP-dispersed solution such as nanofluid with high volume content of NPs, even though the surfaces of NPs are modified because perfect dispersion is defined as the state in which all the NPs are separated from one another and dispersed. The surface-modified NPs may suffer agglomeration and flocculation in solution especially at relatively high NP concentration. As a result of the agglomeration and/or flocculation, the NPs subsequently lose the nanosized properties. Therefore, the proper designs on aim to obtain the perfect dispersion of NPs must be developed. Recently, we reported that the size and size distribution of the fatty acid surface-modified CeO2 NPs strongly affect their dispersion in cyclohexane.6 NPs with adequate size and narrow size distribution showed perfect dispersion up to at least 20 wt %, r 2011 American Chemical Society

i.e., 2 vol %. In other words, poor dispersion was observed for the CeO2 NPs with larger size and broad size distribution. Interestingly, the poor dispersion was improved by adding the perfectly dispersed CeO2 NPs with adequate size and narrow size distribution. This indicates that the size and size distribution of NPs are important parameters to be considered for designing the perfectly dispersible NPs. The next goal is to clarify the requirements on surface modification of NPs to achieve perfect dispersion of NPs. A detailed characterization and quantification of surface-modifying molecules on NPs are absolutely necessary. The densely arrayed surface modifier layers on NPs can be regarded as one of the threedimensional (3D) self-assembled monolayers (SAMs),7-9 e.g., n-alkanethiolates on noble metals,10-24 phosphoric acid derivative surfactants on metal and metal oxides,25-27 and alkanoic fatty acids on metal and metal oxides.28-33 These 3D SAMs on NPs were employed not only to study the dry-state properties of SAMs by increasing the total surface area of SAMs but also to stably disperse NPs in solvents. The dry-state properties of SAMs have been well understood as a result of numerous studies exploring their chemical and physical properties. However, the solution-state behavior of SAMs has not been well investigated and understood. Received: October 24, 2010 Revised: January 19, 2011 Published: February 23, 2011 3899

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The Journal of Physical Chemistry C To explore the solution-state behavior of SAMs, we have previously reported that the purity of the SAM was important for determining its solution-state properties and developed an efficient method to purify SAMs.34 Especially for fatty acid SAMs, it had been quite difficult to purify without losing the graft density of the fatty acid. After the method was established, dry state properties of fatty acid SAMs such as thermally induced phase transition of the SAMs showed good agreement with the theoretically predicted transition; i.e., the fatty acid SAMs showed graft density dependent phase changes.6,34,35 Furthermore, we investigated the solution-state properties of a SAM for the first time using our quasi-crystalline SAMs (SAMs in the highest graft density region) on hybrid CeO2 NPs (HNPs) by using solution-state differential scanning calorimetry (DSC) combined with solution-state NMR which is a distinguished method19 to survey the properties of 3D SAMs.34 As a result, it was found that the quasi-crystalline SAMs swelled in their good solvents and showed a size exclusion effect to the solvent molecules. We also observed strong trapping of the solvent molecules inside the SAMs due to strong osmosis inside the SAMs. The SAMs did behave quite differently in the solution state than in the dry state. Although the dry-state property of SAM can be simply scaled according to the graft density,35 it is complicated in the solution state. Here, we analyzed the detailed features of the molecular motion of 3D SAMs in the solution state. To investigate the effect of chain length and solvents, the various solution states composed of C6-, C10-, and C18-SAMs and several solvents were investigated. The variety of solution-state behaviors were analyzed by NMR and DSC and elucidated in terms of the interaction parameter between the SAM and solvent. By refining the scaling theory to explain the solution-state behavior of polymer brushes, it was possible to successfully characterize the solution-state behavior of SAMs in terms of the chain length, packing density, and solvent quality. Finally, we found a criterion for effective SAMs to obtain perfect dispersion of surface-modified NPs in an organic solvent. The balance between the phase of 3D SAMs on the HNPs and the size, size distribution, and morphology of HNPs was one of the key factors to determine dispersion of the HNPs. The fully swollen (activated) SAMs which showed activated molecular motion in solvents could produce the effective repulsive force between the SAMs, like high density polymer brushes do, to overcome the van der Waals attraction between HNP cores, whereas the unactivated SAMs on HNPs could not. To the best of our knowledge, this is the first study clarifying the relation between the behavior of SAMs on NPs and the dispersion of surface-modified NPs in solution. The findings of this study will be useful for the fundamental understanding of the dispersion of surface-modified NPs in solution and for designing welldispersible NPs.

’ EXPERIMENTAL METHODS Materials. Cerium hydroxide (Ce(OH)4), cyclohexane (99.5%), and benzene (99.8%) were obtained from Sigma Aldrich, while hexanoic acid (99%), decanoic acid (99%), octadecanoic acid (99.5%), hexane (96%), ethanol (99%), acetone (99%), and dichloromethane (anhydrous, 99.8%) were obtained from Wako Pure Chemical Industries. They were used as received. Purified water purchased from Daiwa Yakuhin was used after filtration. Chloroform-d (99.8 atom % D), benzene-d6 (99.6 atom % D),

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cyclohexane-d12 (99.6 atom % D), and tetramethylsilane (TMS, 99.9%) were obtained from Sigma Aldrich and used as received. Synthesis of Hybrid CeO2 NPs (C6-, C10-, and C18-HNPs). Surface-modified hybrid CeO2 NPs (C6-HNPs, C10-HNPs, and C18-HNPs) were prepared by the supercritical hydrothermal method.34 An amount of 2.5 mL of a 0.1 M cerium hydroxide aqueous suspension and a surface modifier were loaded into a pressure-resistant Hastelloy reactor (inner volume: 5 mL). Hexanoic acid (0.184 g), decanoic acid (0.267 g), and stearic acid (0.426 g) were used as modifiers to synthesize C6-, C10-, and C18HNPs, respectively. The hydrothermal reaction was carried out at 400 C for 10 min and terminated by submerging the reactor into a water bath. The surface-modified NPs were extracted with hexane (3 mL) from the aqueous product mixture. The organic portion was collected, and ethanol (12 mL) was added to remove the residual modifier. HNPs were collected by centrifugation and carefully freeze-dried. Further purification was carried out by a poor solvent precipitation method. The obtained nanoparticles could be redissolved in various organic solvents such as cyclohexane, toluene, and chloroform. The purified and dried HNPs were stored and handled inside an oxygen- and moisture-free glovebox. Characterization. Transmission Electron Microscopy (TEM). The THF solution of HNPs was dropped onto a standard carbon-coated copper grid and dried at room temperature. Electron micrographs were obtained using a Hitachi H-7650 microscope at an accelerating voltage of 100 kV. The particle sizes were calculated from the average of more than 300 particles using the image analysis software program SigmaScan Pro4 (Jandel Scientific). Fourier Transfer Infrared Spectroscopy (FT-IR). HNPs were deposited onto a KBr disk, and their spectrum was measured using a Jasco FT/IR 680 plus spectrometer. Spectra were recorded in the absorbance mode at a resolution of 4 cm-1 at room temperature. Dynamic Light Scattering (DLS). DLS was performed using a Malvern Zetasizer Nano ZS particle size analyzer. The general purpose (GP) analysis function in the Zetasizer Nano software, a nonnegative least-squares (NNLS) algorithm, was employed to obtain the average diameter distribution of the dispersant in organic solvents. Thermal Analyses. The thermogravimetry (TG) analysis was carried out in Ar (flow rate = 30 mL/min) at a heating rate of 10 C/min using a Rigaku TG-DTA 8120 system. The surface coverage of HNPs was calculated from the weight loss and the average diameter of the HNP core, assuming the core to have a truncated cubic shape. Differential scanning calorimetry (DSC) was carried out with a TA Instruments Q100 system. An amount of 10 mg of HNP solution (4 mg of HNPs in 6 mg of solvent) was loaded into a high-pressure vessel. The thermograms were run with a temperature sweep of 5 or 10 C/min under nitrogen flow (flow rate = 50 mL/min). Three cycles were repeated for every DSC measurement to check repeatability. The chart corresponding to the second cycle is shown. Nuclear Magnetic Resonance (NMR). The solution-state 1H NMR spectra were obtained using a 400 MHz JEOL FT-NMR system, JNM-ECX40, with a temperature control unit. To evaluate the molecular motion of SAMs in various solvents, the integral values of their signals were compared. TMS and dichloromethane were used as the standards for integral analysis because their chemical shift peaks in the deuterated solvents used in this 3900

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study do not overlap with the original peak of HNPs (0.00 ppm for TMS and 5.30 ppm for dichloromethane). Amounts of 1 μL of TMS and 1 μL of dichloromethane were dissolved in 25 μL of CDCl3, after which the solution was loaded into a capillary tube. For HNP solutions, 5 mg of each HNP was dissolved in 500 μL of the desired deuterated solvent (around 1 wt % HNP solution of CDCl3, C6D6, and C6D12). The HNP solution was then loaded into an NMR tube, and a flame-sealed capillary tube was located in the NMR tube (see Supporting Information). The sample liquid levels in the NMR tube and in the capillary were both adjusted to 45 mm. The spectra of the sample were recorded with 32 times accumulation. The chemical shifts and integrals of the sample peaks were calculated by setting the chemical shift of the TMS peak as 0.00 ppm and the integral values of TMS and dichloromethane peaks as unity. To obtain the net integral value of HNPs, the background signals from residual solvents, moisture, and impurity were subtracted.

’ RESULTS AND DISCUSSION 1. Preparation of n-Alkanoic Acid SAMs on the HNPs. The hybrid CeO2 NPs (HNPs) were synthesized and purified using the supercritical hydrothermal method.34 Details of the procedure are described in the Experimental Section. In this study, we used various n-alkanoic acids (hexanoic, decanoic, and stearic acids) as modifiers to synthesize various HNPs. The samples are abbreviated as C6-, C10-, and C18-HNPs, indicating the number of carbon atoms in the alkanoic acid chain on HNPs. Residual modifiers should be eliminated because even a small amount of residual modifier can seriously affect the properties of SAMs and the dispersion of HNPs in solvents.6 To eliminate residual modifiers and obtain the quasi-crystalline 3D SAMs on HNPs, the poor solvent precipitation method was applied to the assynthesized HNPs.34 As seen in the FT-IR spectra of Figure 1(a), the absence of the peak due to the free carboxyl CdO stretching mode (1700 cm-1) indicates that the 3D SAM on HNPs was wellpurified and did not have any residual or weakly bound alkanoic acids.34 Three peaks corresponding to the symmetric (1445 and 1414 cm-1) and asymmetric (1532 cm-1) stretching of the carboxylate anion were observed in all three samples. The peak intensity of symmetric (2850 cm-1) and asymmetric (2920 cm-1) stretching of CH2 in the HNPs increased with the carbon number in the n-alkanoic acid. These results suggest that all HNPs have well-purified n-alkanoic acid SAMs that are constructed only by strongly chemisorbed alkanoic acids on the Ce atoms of the (001) surface of the CeO2 crystal.36 The solid structure of a SAM in the dry state is defined along with its packing density, λ, i.e., the graft density divided by maximum graft density (here, packing density is defined as λ = the graft density/the maximum graft density), according to the scaling theory.35 At low packing densities (e0.2), SAMs are in an amorphous state wherein alkyl chains are essentially oriented parallel to the surface. At medium packing densities (0.2 e λ e 0.75), alkyl chains are intermediately ordered, and SAMs are in a semicrystalline state. At high packing densities (g0.75), SAMs form a quasi-crystalline structure, and the tilt angles of alkyl chains relative to the surface normal are smaller than 30. The maximum packing density of alkanoic acid chains cannot exceed the bulk density of the alkanoic acid in the crystalline state. From the crystal structure analysis of n-alkanes, the cross section of an alkyl chain in the packed crystal is the constant value of 0.188 nm2, at room temperature.37,38 This means that the maximum density of alkyl

Figure 1. (a) FT-IR spectrum and (b) TG-weight loss of C6-, C10-, and C18-HNPs. The arrows (i), (ii), and (iii) represent the peak corresponding to the asymmetric (1532 cm-1) and symmetric (1445 and 1414 cm-1) stretching of the carboxylate anion, respectively.

chains in the SAM is limited to 5.32 chain/nm2 (0.188 nm2/chain). The graft densities of the SAMs on the HNPs were calculated using the HNP core sizes from TEM images and weight fractions of the SAMs from TG weight loss.34 Because the HNPs in this study had almost cubic shape (see Supporting Information, the TEM images were depicted), we regarded the shapes of HNPs as cubic and calculated the diameter of each HNP core assuming it to be the same value as the edge length. The average diameters of the three HNPs were 4.69 ( 0.61, 6.54 ( 0.85, and 7.07 ( 1.23 nm for C6-, C10-, and C18-HNPs, respectively. From the TG weight losses of 14.1%, 14.9%, and 20.3% for C6-, C10-, and C18-HNPs, respectively (Figure 1(b)), the average grafting densities of the three n-alkanoic acid SAMs were calculated to 4.96, 4.97, and 4.85 chains/nm2, respectively (see Supporting Information for detailed calculations). Thus, the SAMs on the HNPs in this study showed relatively high packing densities of 0.93, 0.93, and 0.91 for C6-, C10-, and C18HNPs, respectively. This indicates that the SAMs on all three HNPs are in the quasi-crystalline state according to the scaling theory.35 Table 1 summarized the average particle sizes, TG weight loss, grafting density, and packing density of the SAMs. 2. SAMs and Dispersion of HNPs in Solvents. 2-1. SolutionState Behavior of SAMs on HNPs. The stability of NP dispersion depends on the balance between the van der Waals attraction from NP cores and the steric repulsion from modifiers on the surface of NPs.39 The behavior of SAMs will be a key factor in controlling the dispersion of HNPs when they are loaded in various solvents. Figure 2 shows images of C10-HNPs in chloroform, benzene, cyclohexane, and decalin at the same concentration of the C10-HNPs 3901

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Table 1. Size, Percentage Weight Loss, Grafting Density, and Packing Density of SAMs on HNPs samples core size (nm)

C6-HNPs 4.69 ( 0.61

wt loss (%) 14.1 grafting density (chains/nm2) 4.96 packing density

0.93

C10-HNPs 6.54 ( 0.85

C18-HNPs 7.07 ( 1.23

14.9 4.97

20.3 4.85

0.93

0.91

Figure 2. Images of C10-HNPs in chloroform, benzene, cyclohexane, and decalin with the same concentration of HNPs (10 mg/mL): (a) 15 min after sample preparation and (b) 2 months after sample preparation.

(5 mg in 500 μL). The dispersion of the C10-HNPs depended on the solvent. The C10-HNPs were well-dispersed in chloroform and cyclohexane for over 2 months. Although the C10-HNPs were initially well-dispersed in decalin, they were precipitated after 2 months. This suggests that the relaxation time required to reach dispersion equilibrium in decalin is relatively long. Benzene also failed to provide perfect dispersion of the C10-HNPs. For further understanding of the drastic differences in the dispersion of the C10-HNPs in solvents, we investigated the solution-state behavior of SAMs on HNPs. As mentioned above, the solution-state properties of SAMs will be a key to understanding the dispersion of HNPs in solvents. The solution-state 1 H NMR spectroscopy was used to analyze the molecular motion of SAMs on HNPs in solvents. Since the integral values of a sharp peak in the 1H NMR spectrum in the diluted solution are proportional to

the concentration of the H atom, integral values of the signals from HNPs could be used to analyze different behaviors of HNPs in solvents. Two standard chemicals, TMS and dichloromethane, were used for the reference peaks whose integral values were set to unity (see Supporting Information). Figure 3 displays the NMR spectra of C10-HNPs in various solvents. First, a comparison of C10-HNPs (5 mg) and free decanoic acid (1 mg) clearly shows a broadening of peaks from the SAMs on the HNPs. While the peak from the terminal methyl group was observed at 0.8-1 ppm, the C1 methylene hydrogen signal was not detected in the spectrum of HNPs. The broad signals around 1.3-1.5 ppm are attributed to the inner methylene groups (C2-C8) of the SAMs. These results indicate that the chains in SAMs are restricted in their motion by binding and are not desorbed in the solvents, at least in our observations.19,21,32,34 Their integral values of 3.1 for HNPs and 6.9 for decanoic acid also point out the restricted motion of SAMs on HNP. In the same manner, we evaluated the molecular motion of the SAMs on HNPs in various solvents. Interestingly, the motion of the SAMs on HNPs is more restricted in benzene than in chloroform and cyclohexane, and it is greatly restricted in decalin. We did not find any large differences between the NMR signals with HNP-decalin solution and decalin as shown in Figure 3(d). The restriction of the motion of SAMs in decalin was supported by the DSC measurement due to the size exclusion effect of SAMs as reported previously.34 The integral values listed in Table 2 indicate that C10-HNPs are most activated in cyclohexane. The activated molecular motion of a SAM in a solvent can be regarded as a swelling of the SAM by its good solvent.34 The penetration of good solvent molecules into SAMs increases the osmotic pressure inside the SAM. Hence the SAMs are stretched, and their molecular motion will be activated. The Flory-Huggins interaction parameter, χ12, is widely used to scale the interaction between a polymer chain and a solvent. An interaction parameter with a value smaller than 1/2 (i.e., χ12 < 1/2) indicates that the solvent is a good solvent for the polymer and the mixing is favorable. When χ12 is 1/2, the solvent is called a Θ solvent. The poor solvent condition is χ12 > 1/2. The interaction parameter can be calculated from the solubility parameters.40 On the basis of regular solution theory, the relationship between the Flory-Huggins interaction parameter and the solubility parameter is defined as41 χ12 ¼

V1 ðδ1 - δ2 Þ2 RT

ð1Þ

Since the solubility parameter is derived from the cohesive energy density, the solubility parameter of a SAM could be different from that of a normal free chain. For a more realistic analysis, two methods of calculating the solubility parameter of a SAM can be considered: (1) treating the SAM chain as a normal n-alkanoic acid and (2) considering only the alkyl chain group of the SAM. Because the anchor group of the SAM is very polar due to its electric charge on the oxygen atoms and the CeO2 crystal surface is hydrophilic, the solvents would not prefer mixing with the anchor group (see Supporting Information). Therefore, method (2) is adequate for predicting the effective interaction between SAMs and solvents. For the calculation of solubility parameters, we applied the group contribution method of van Krevelen.42 Detailed calculations and the calculated solubility parameters are listed in the Supporting Information. 3902

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Figure 3. 1H NMR (400 MHz) spectra of C10-HNPs in various deuterated solvents. (a) Comparison of spectra of free decanoic acid (1 mg) and HNPs (5 mg) in 500 μL of CDCl3. The carbon numbering is indicated in the upper left corner. (b) HNPs in C6D6 and CDCl3, (c) HNPs in C6D12 and C6D12, and (d) HNPs in C10D18 and C10D18. The concentration of HNPs in all solvents was 10 mg/mL. All spectra were recorded with 32 times accumulation.

Table 2. Integral Value of Solvents and Sample Solutions in the NMR Spectrum C6-HNPs a

C10-HNPs

C18-HNPs

CDCl3

1.9 (0.028)

3.1 (0.038)

4.3 (0.034)

C6D6

1.7 (0.025)

2.2 (0.027)

2.7 (0.022)

C6D12

1.3 (0.019)

3.9 (0.048)

4.2 (0.033)

a

The number in the parentheses is the value normalized to the concentration of the SAMs and the total number of H atoms in the SAM. For example, 3.1/(4.3 [μmol]  19) = 0.038 for C10-HNPs in CDCl3.

Figure 4 displays the interaction parameters between decanoic acid and various solvents and between the alkyl group of C10-SAM and the same solvents. The interaction parameter between free decanoic acid and the solvents except for cyclohexane showed small values; i.e., they have strong affinity. Cyclohexane showed the highest interaction parameter with decanoic acid. This is apparently contradictory to our observation that the SAM is most activated in cyclohexane. On the other hand, method (2), which considers only the alkyl chain group of the SAM, gave a better evaluation of the affinity of solvent molecules for the SAM. The interaction between the alkyl group of the SAM and the solvents helps to explain the differences in the behavior of the SAM depending on the solvents. In particular, cyclohexane shows the strongest interaction with the alkyl group of the SAM. This strong affinity encourages cyclohexane molecules to penetrate the SAM despite their relatively large molecular size. Therefore, the SAM is swollen, and the molecular motion in the SAM is activated in cyclohexane. As we previously reported that decalin molecules are too large to penetrate in the

Figure 4. Interaction parameter between SAMs and various solvents and molecular volume of solvents. The opened data points indicate the interactions between free n-alkanoic acids and solvents. The closed data points indicate those between the alkyl groups of SAMs and solvents.

densely packed SAM, thus the SAM was not swollen in decalin,34 the interaction between the SAM and decalin is not strong enough to overcome the disadvantage from its large molecular volume. The relatively restricted molecular motion of the SAM in benzene can also be explained in terms of its weaker affinity for the alkyl group of the SAM, even though it has smaller molecular size. We also investigated the chain-length-dependent changes in the behavior of HNPs in the same manner. Figure 5 shows the NMR spectra of C6-, C10-, and C18-HNPs in various solvents. Their molecular motions in various solvents can be compared by 3903

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Figure 5. 1H NMR (400 MHz) spectra of HNPs in various deuterated solvents: (a) C6-HNPs, (b) C10-HNPs, and (c) C18-HNPs in C6D12, C6D6, and CDCl3. The concentration of HNPs in all solvents was 10 mg/mL. All spectra were recorded with 32 times accumulation.

the integral values of their peaks as shown in Table 2. The interaction parameters between the SAMs and solvents are described in Figure 4. In other words, integral values of NMR peaks and interaction parameters showed good correlation by assuming the SAMs were constructed by an assembly of alkyl chains: when the interaction parameter was small, the molecular motion of SAMs was activated. The result suggests that the effective interaction between SAMs and solvents could be estimated by regarding the SAM as an assembly of the alkyl chains; i.e., the anchor group is not important because it is too polar. A good solvent and a small molecular size of a solvent are required for the solvent molecules to swell the SAMs. The penetrated solvent molecules increase the osmotic pressure inside the SAM, and therefore, the SAM will swell to maintain the balance between the osmotic pressure and the conformational entropic force. Consequently, the molecular motion of

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alkyl chains will be activated, and then solution state NMR spectroscopy can be used to detect the extent of the activation. The extent of the solvent penetration could be examined by DSC analysis.34 The DSC cooling curves of various HNP solvent systems are shown in Figure 6. The small exothermic peak was present around -5 C just after the large latent heat peak according to freezing of cyclohexane (∼0 C) in the C10- and C18-HNPs solutions. This small exothermic peak became smaller and shifted to a higher temperature when cooling rate was lowered to 5 C/min. This could be caused by the cyclohexane molecules captured in the SAMs.34 As expected from the interaction parameters and NMR analysis, the C6-HNPs solution showed only one peak attributed to free cyclohexane molecules. Besides, the small exothermic peak for the benzene solutions was not observed even at a cooling rate of 10 C/min. This implies that the solvent molecules were not really penetrated in the SAMs to give rise to a small additional peak. When the osmotic pressure inside a SAM is increased by the penetration of solvent molecules, the SAM will swell to balance between the osmotic pressure and the conformational entropic force. This stretched state can be given the same physical meaning with the swelling of the polymer brush; i.e., it can be regarded as a swollen state of SAMs in which SAMs exhibit their activated molecular motion in solvents. When the penetration of solvent molecules into a SAM is unfavorable, the SAM cannot be stretched and does not gain the conformational entropic force. This can be regarded as a collapsed structure of SAMs. 2-2. Contribution of SAMs on Dispersion of HNPs. The solution-state behavior of SAMs on HNPs has a strong influence on the dispersion of HNPs in solvents. It is apparent that the well-dispersed HNPs displayed in Figure 2 have swollen SAMs in the solution. It is very important to know whether the SAM is swollen or not to evaluate the steric repulsion between the SAMs, an important repulsive force to disperse HNPs. Steric repulsion is caused by the interpenetration of two modified layers when they start to overlap. However, quasi-crystalline SAMs would not interdigitate with each other due to their high packing density even when they are compressed. de Gennes has derived the interaction force between two flat surfaces with dense polymer brush layers which do not interpenetrate each other.43 This polymer brush model will be adequate for our system to evaluate the repulsive force between HNPs. The force per unit area between two polymer brushes is given by the following equation kT FðdÞ ¼ 3 S

"

2le d

9=4



d 2le

3=4 # d < 2le

ð2Þ

where S is the average distance between chains directly calculated from the grafting density; le is the equilibrium thickness of the brush; and d is the surface-to-surface distance. The first term is the osmotic term stretching the polymer chains, which produces a repulsive force under compression. The second is the elastic term shrinking the SAMs. Under strong compression, the osmotic term becomes very large and dominant. It should be noted that the equilibrium thickness of the brush, le, is the critical distance where the repulsive force becomes effective. In the case of SAMs, their equilibrium length in solvents is determined by the balance between the osmotic pressure stretching SAMs and the configurational entropy that forces the SAMs to collapse. Therefore, the stretched SAMs (swollen SAMs) will provide stronger repulsion. 3904

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Figure 6. DSC cooling curves for 40 wt % solutions of HNPs. C6-, C10-, and C18-HNPs (a) in cyclohexane with a 10 C/min cooling rate, (b) in cyclohexane with a 5 C/min cooling rate, and (c) in benzene with a 10 C/min cooling rate.

Figure 7. Total potential curves between two HNPs. The repulsion caused by the SAMs on the surfaces of HNPs becomes effective when the SAMs start to overlap each other.

To obtain the total energy of two SAMs when they approach each other, their overlapping area was multiplied at each distance. Therefore, the total potential between two HNPs could be written as Etot ¼ EvdW þ FðdÞ  AðdÞ

ð3Þ

The calculated total potential curves between two HNPs in cyclohexane are shown in Figure 7 (see Supporting Information for detailed calculations). The van der Waals force is varied with core size; i.e., smaller core produces weaker attractive force. To evaluate the influence of extent of the swelling of the SAMs on steric repulsion between SAMs, the potential energy curve between HNPs when SAMs are not fully swollen was calculated for C10-HNPs. As expected, the position where the repulsive force was activated became closer to the HNP core. The dispersion of HNPs in benzene or decalin can be better understood using this model because the SAMs are not fully swollen in benzene and decalin. The dispersion of C18-HNPs appears to be worse than that of C10-HNPs, even though they have longer SAMs on their surfaces. This unstable dispersion can be understood by the size effect of the C18-HNP cores. As we reported previously, since the size and the size distribution of C18-HNPs cores are slightly large and broad, the net potential between HNPs is unbalanced, and

perfect dispersion cannot be achieved.6 The integral values of the NMR signals correlated well with the dispersion of HNPs. The integral values listed in Table 2 were normalized by the actual concentration of the SAM in solution and the total number of H atoms in the SAM. Under well-dispersed conditions such as C10HNPs in chloroform or cyclohexane, the normalized value was large, which indicates that the molecular motion of the SAMs was highly activated. Note that although C6-HNPs have short SAMs (maximum length: 0.76 nm) the repulsion appears to be sufficient for overcoming the van der Waals attraction since the small core size of C6-HNPs produces a relatively small attractive force. However, C6-HNPs did not disperse well in any solvents and showed white turbidity indicating flocculation of HNPs (Figure 8). This deviation from the prediction from the scaling theory suggests that the solution-state behavior of C6-SAMs has to be understood as a different case. The solution-state behavior of SAMs on HNPs seriously affects the dispersion of HNPs in solvents. The activated SAMs (i.e., swollen SAMs) can provide a good repulsion barrier against the van der Waals attraction between the HNP cores. The swollen SAM by solvent molecules is required to achieve good dispersion of HNPs in solution. 3. Design of SAMs for Good Dispersion of HNPs. 3.1. Modified Scaling Approach for SAM and Polymer Brush. Previous reports on the dry-state behavior of the SAM suggest that the major changes in the structure of SAMs occur somewhere between n = 5 and n = 11 (n is the number of carbon atoms in the alkyl chain) because shorter alkyl chains are more disordered.10,28,44 However, the model for the structure of SAMs suggested by Heinz et al. can be applied only to SAMs whose alkyl chain is longer than C10, and the changes depending on chain length have not been considered. It seems that this classification is too rough for describing the nature of the SAM. The chain-length-dependent changes of SAMs may be worth examining closely. In fact, C8-SAMs on the several kinds of NPs (Ag, Au, and Cu) have been already reported.18,21,45 Furthermore, even the C6 alkyl chain has been used as a capping ligand for organic monolayer-stabilized NPs.46,47 Therefore, it is necessary to construct a comprehensive model that considers all three important factors, i.e., graft density, chain length of a SAM, and the solvent quality. A detailed understanding of the solution-state 3905

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Figure 8. Images of various HNP solutions. C6-, C10-, and C18-HNPs in (a) CDCL3, (b) C6D6, and (c) C6D12. The images were taken 1 h after the sample preparation.

behaviors of SAMs will be useful for designing highly dispersible surface-modified NPs. Using a scaling approach, the end-to-end length of a linear polymer chain in a diluted solution, i.e., the Flory radius (RF), can be calculated by RF ¼ b 3 N ν

ð4Þ

where b is the length of the monomer (0.126 nm for alkyl chain); N is the total number of monomers in the chain; and ν is called the Flory exponent.48 This is obtained from minimizing the free energy constructed by two terms, the osmotic pressure due to the interaction between the monomer and solvent molecules and the configuration entropy of a chain. When the monomer-solvent interaction is more attractive than the monomer-monomer interaction, the chain swells leading to a large value of ν. ν = 0.5 in the condition of Θ solvent, and v = 0.6 for good solvent.49,50 For relatively short chains in a good solvent, ν = 0.655 has been suggested by many theoretical studies and simulations (Figure 6 of ref 49).51 This relatively large value of the Flory exponents is probably due to the fact that the short chain forms a near-linear structure rather than a coil-like structure. When the graft density is sufficiently high and the distance between grafting points, S, is smaller than RF, the chains will be stretched and form the polymer brush structure to avoid overlapping between them. On the other hand, the chains do not interact with each other and form a mushroom structure when S > RF.52 Interestingly, it is impossible for C6-SAM to form a brush-like structure even at the perfect packing (RF/S = 0.86). In other words, C6-SAM has to be in the collapsed state. Hence, its thickness le would be shorter than 0.76 nm. In fact, Porter et al. reported that the thickness of C6-SAMs is shorter than its fully extended length in the dry state.12 Note that the minimum chain length (>C8) is required even at the high packing densities (g0.75) for a SAM to form a polymer brush-like (quasi-crystalline) SAM which provides effective repulsion. In the case of longer chains, it is easier to form the polymer brush structure even at a low packing density. For example, a low packing density (0.4) is enough to form a polymer brush structure for C18-SAM (RF/S = 1.22). The structure of SAMs in the solution state is strongly dependent not only on packing density but also on chain length. For the solvent quality effect, when the Flory exponents are small as in the Θ solvent condition, the scaling criteria for a polymer brush like SAM become more severe, since the size of RF decreases.

Figure 9. Different modes of alkyl chains grafted on the surface depending on packing density and chain length under good solvent conditions: mushroom structure (amorphous), semidilute polymer brushes, concentrated polymer brushes, and SAMs. The red region indicates the polymer brush like SAMs when RF g S.

At low packing densities (e0.2), a longer chain (>C23) is required to form a polymer brush like SAM. This region will extend to the real polymer brush, which is constructed by longer chains of high molecular weight. Since the behavior of a longer chain in solution is different from that of a short linear chain, the SAM would be expected to exhibit different behavior when the chain length becomes longer. To scale the size of a longer polymer chain in a solution, the radius of gyration is generally used because of their random coil structure.53 The ratio between the end-to-end distance RF and the radius of gyration Rg of a polymer chain is found to be54 ÆRg2 æ=ÆRF2 æ ¼ 1=6

ð5Þ

This ratio is independent of N. Thus, the radius of gyration of a polymer chain in a good solvent can be obtained from RF using a value of 0.6 for the Flory exponent. We can then suggest a boundary where two grafted polymer chains start to overlap. When the distance between grafting points, S, is smaller than 2Rg, the chains will be stretched and start forming the polymer brush structure to avoid overlapping between them. When S is larger than 2Rg, the grafted polymer chains form a mushroom structure. This criterion is well consistent with the experimental data of 3906

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Figure 10. Three-dimensional graph of RF/S ratio as a function of packing density and number of carbons in the alkyl chain for (a) ν = 0.655 under good solvent condition and (b) ν = 0.5 under Θ solvent condition. (c) Images of 1 wt % solution of sparsely covered C10-HNPs and 5 wt % solution of normal C10-HNPs in cyclohexane. (d) DLS measurements of HNP solutions in (c). All images and DLS data were obtained 15 min after the sample preparation.

polymer brushes obtained from previous reports (see Supporting Information). Figure 9 illustrates the different modes for grafted alkyl chains on the surface using a scaling approach. When grafted chains are sufficiently long, they form a brush-like structure. As mentioned above, grafted chains remain in a mushroom structure when their coils do not overlap. The boundary of 2Rg/S = 1 (i.e., the overlapping condition of coils) has the same physical meaning with the semidilute polymer solution condition. As the packing density increased, a high-order interaction between grafted chains occurs, and the chains are strongly stretched. In addition, they generate strong repulsion against the compression due to the high osmotic pressure inside them. This state is called the concentrated brush. Although it is difficult to define the boundary between the concentrated polymer brush and the semidilute polymer brush, a packing density of 0.1 could be suggested as a boundary according to experimental studies on the chain strength of polymer brushes in good solvents55-58 (see Supporting Information). Compared with polymer brushes, the SAM region is limited to the relatively short chains and a high packing density to form sufficiently distinctive patterns on the surface.53 Interestingly, SAMs do not have an intermediate range as do polymer brushes. They go directly through the transition from an amorphous (mushroom structure) to an assembled structure. As their chain length increases, their behavior will be close to that of the polymer brush. Although the accurate identification on the linking between SAMs and polymer brushes is difficult because of lack of experimental data,

this unexplored area would be important for understanding the general behavior of the grafted chains and for designing the surfacemodified layers that can generate strong repulsion against the compression and improve the dispersion of NPs. Nonetheless, our present study is sufficient to predict conditions for obtaining a concentrated polymer brush-like stretched SAM. This condition, RF/S g 1, is shown in the red region of Figure 9. The polymer brush-like SAMs can provide effective repulsion against compression due to high osmotic pressure inside them. Therefore, this criterion should be satisfied when we intend to disperse NPs by coating their surfaces with SAMs. 3.2. Design of Good Dispersible HNPs. Figure 10(a) illustrates a three-dimensional graph of the RF/S ratio depending on packing density and chain length (carbon number in the chain). When RF/S < 1 (the gray range), a SAM cannot form a polymer brush-like structure. This modified scaling approach can explain the bad dispersion of C6-HNPs in solvents. The distance between C6-chains is not sufficiently small to stretch the chains and to form a polymer brush like structure even at the maximum packing density. Therefore, the C6-SAMs on C6-HNPs cannot provide effective repulsion. This is consistent with our NMR and DSC results for the solutionstate behavior of SAMs, i.e., restricted molecular motion and no swelling of the SAMs due to the low osmotic pressure inside them. The unstable dispersion of HNPs in benzene can also be understood in the same manner. In the case of benzene, it is not a good solvent for the SAMs and would have a small value of the Flory exponent as displayed in Figure 10(b). 3907

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The Journal of Physical Chemistry C To assess the validity of this scaling criterion for good dispersion of HNPs, we investigated the solution-state behavior and dispersion of sparsely covered HNPs (with low density SAMs). The sparsely covered C10-HNPs were synthesized and purified according to a previously reported method.52 The average core size was 4.54 ( 0.66 nm, and the graft density was 2.92 chains/nm2 calculated from 12.75% of TG weight loss (see Supporting Information). The distance between graft points increased to 0.58 nm. The ratio RF/S was 0.98, suggesting that the SAMs cannot form a polymer brush structure according to the scaling approach. In other words, the SAMs on the sparsely covered HNPs have a mushroom structure with a packing density of 0.55. NMR and DSC analyses on their solution-state behavior also supported that the SAMs have a collapsed structure. The integral value of NMR peaks corresponding to the alkyl groups of the SAM was very small. Furthermore, the additional peak on the cooling curve of the solution-state DSC due to penetrated solvent molecules was not detected even at a 10 C/min cooling rate (see Supporting Information for detailed characterizations). From the dry-state DSC analysis of the sparsely covered SAM on HNPs, we previously showed a reversible thermal transition on the DSC heating curve occurring in the semicrystalline C10-SAM on HNPs (2.89 chains/nm2).52 These results indicate that the SAM is collapsed and did not have sufficient osmotic pressure to stretch the alkyl chains in the solvent. Therefore, the repulsion between sparsely covered C10-HNPs will not be sufficient to overcome the van der Waals attraction from the HNPs cores. As expected, the dispersion of sparsely covered C10-HNPs in cyclohexane was much poorer than that of normal C10-HNPs, as shown in Figure 10(c). Although the van der Waals attraction between sparsely covered C10-HNPs is weaker than that of normal C10-HNPs, because of the smaller core and narrow size distribution of the former, they did not perfectly disperse in 1 wt % solution. In contrast, the densely covered (normal) C10-HNPs showed perfect dispersion with single NPs even at 5 wt % concentration as seen from the DLS measurements shown in Figure 10(d) and up to at least up to 20 wt % as reported in elsewhere.6 Simply decreasing the packing density of the SAMs drastically changed the dispersion behavior of HNPs in solution. Therefore, the solution-state behavior of SAMs is one of the critical factors for designing surface-modified NPs in solvents. Our criterion for the SAMs would be useful to obtain welldispersible NPs.

’ CONCLUSIONS We have succeeded in exploring the solution-state behavior of the 3D SAMs on the CeO2 NPs. Their solution-state behavior is complicated and dependent on various parameters, i.e., chain length, packing density, solvent quality, and solvent molecular volume. A good affinity for the SAM chains and a small molecular size of solvents to penetrate the SAM are necessary to swell SAMs and increase the osmotic repulsion force between them. The detailed features of swollen SAMs under various conditions were analyzed by NMR and DSC analyses. Furthermore, the effect of chain length and packing density on NP dispersion was investigated using a scaling approach. The solution-state behavior of grafted chains was categorized into the mushroom structure (amorphous), semidilute polymer brushes, concentrated polymer brushes, and SAMs. This scaling approach was useful in predicting the solution-state behavior of SAMs, i.e., whether a SAM will behave as a polymer brush or not.

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Finally, a criterion for a SAM to achieve good dispersion of NPs is suggested by combining the scaling analysis with our observations on the behavior of the SAMs. The dispersion of HNPs drastically changed depending on the condition of SAMs since only swollen SAMs can provide effective repulsion. By examining the relation between the dispersion of NPs and the behavior of SAMs grafted on them, we found that polymer brushlike SAMs on NPs were required for the stable dispersion of NPs at a high concentration. The results of this study will be useful for designing well-dispersible NPs and obtaining a stable nanofluid with highly concentrated NPs.

’ ASSOCIATED CONTENT

bS

Supporting Information. Detailed descriptions of the experimental methods, calculation methods, and results were included. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: þ81-22-217-5630. Fax: þ81-22-217-5631. E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by a Scientific Research Grant from the Ministry of Education, Science, Sports, and Culture of Japan. This research was also partly supported by New Energy and Industrial Technology Development Organization Japan (NEDO). The author (T. Arita) thanks Grant-in-Aid for Young Scientists (B) No. 19750094 for their financial support. The author, J. Yoo, is grateful to WPI-AIMR for a graduate research assistant fellowship. ’ REFERENCES (1) Barrera, C.; Herrera, A. P.; Rinaldi, C. J. Colloid Interface Sci. 2009, 329, 107–113. (2) Iijima, M.; Kamiya, H. J. Phys. Chem. C 2008, 112, 11786–11790. (3) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706–8715. (4) Puntes, V. F.; Krishnan, K. M.; Alivisatos, A. P. Science 2001, 291, 2115–2117. (5) Studart, A. R.; Amstad, E.; Gauckler, L. J. Langmuir 2007, 23, 1081–1090. (6) Arita, T.; Yoo, J.; Ueda, Y.; Adschiri, T. Nanoscale 2010, 2, 689–693. (7) Badia, A.; Lennox, R. B.; Reven, L. Acc. Chem. Res. 2000, 33, 475–481. (8) Ulman, A. Chem. Rev. 1996, 96, 1533–1554. (9) Siloxane SAMs on SiOx surfaces are also very popular SAMs; however, siloxanes easily cross-link to form a different type of selfassembled structure than thiolates and alkanoic acids, and therefore they are not discussed in this manuscript. The same treatment was done in ref 7. For the structure of self-assembled siloxanes, see, e.g.: Allara, D. L.; Parikh, A. N.; Rondelez, F. Langmuir 1995, 11, 2357–2360. (10) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559–3568. (11) Bain, C. D.; Whitesides, G. M. J. Am. Chem. Soc. 1988, 110, 3665–3666. (12) Bain, C. D.; Troughton, E. B.; Tao, Y. T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G. J. Am. Chem. Soc. 1989, 111, 321–335. 3908

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